Stochastic stability for nonlinear systems driven by Lévy noise
Stochastic stability for nonlinear systems driven by Lévy noise
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DOI：
10.1007/s11071-011-0199-8
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发表时间：
2012-04
影响因子：
5.6
通讯作者：
Yong Xu;Xiying Wang;Huiqing Zhang;Wei Xu
中科院分区：
文献类型：
--
作者：
Yong Xu;Xiying Wang;Huiqing Zhang;Wei Xu
基于李雅普诺夫指数研究了具有Lévy过程的非线性系统的随机稳定性。提出了一种等效线性化的方法，以减少和简化原系统。最后通过均方响应的计算验证了该方法的有效性。然后定义并推导了系统的李雅普诺夫指数，并给出了两个例子来说明等价线性化的过程，并对这两个特例进行了随机稳定性分析。结果表明，等效线性化技术可用于研究Lévy噪声激励下的非线性系统。
This paper is to investigate the stochastic stability for nonlinear systems with Lévy process based on Lyapunov exponents. A method of equivalent linearization is proposed to reduce and simplify the original systems. And the mean square responses are carried out to verify the effectiveness of the proposed approach. Then the Lyapunov exponents will be defined and derived to explore the stochastic stability, and two examples are presented to demonstrate the procedure of equivalent linearization and stochastic stability is considered for these two special examples. The results show that the technique of equivalent linearization can be used to study nonlinear systems excited by Lévy noise.